Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\left(x \cdot \left(x + y\right)\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\left(x \cdot \left(x + y\right)\right) \cdot 2
double f(double x, double y) {
        double r583551 = 2.0;
        double r583552 = x;
        double r583553 = r583552 * r583552;
        double r583554 = y;
        double r583555 = r583552 * r583554;
        double r583556 = r583553 + r583555;
        double r583557 = r583551 * r583556;
        return r583557;
}
↓
double f(double x, double y) {
        double r583558 = x;
        double r583559 = y;
        double r583560 = r583558 + r583559;
        double r583561 = r583558 * r583560;
        double r583562 = 2.0;
        double r583563 = r583561 * r583562;
        return r583563;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x + y\right)\right) \cdot 2}\]

  3. Final simplification0.0

    \[\leadsto \left(x \cdot \left(x + y\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2) (+ x y))

  (* 2 (+ (* x x) (* x y))))